We describe and evaluate the application of a spectral clustering technique (Ng et al., 2002) to the unsupervised clustering of German verbs. Our previous work has shown that standard clustering techniques succeed in inducing Levinstyle semantic classes from verb subcategorisation information. But clustering in the very high dimensional spaces that we use is fraught with technical and conceptua...

For spoken term detection, it is crucial to consider out-ofvocabulary (OOV) and the mis-recognition of spoken words. Therefore, various sub-word unit based recognition and retrieval methods have been proposed. We also proposed a distant n-gram indexing/retrieval method for spoken queries, which is based on a syllable n-gram and incorporates a distance metric in a syllable lattice. The distance ...

In this paper, we show how to address the asymptotic behavior of the mutual information of correlated MIMO Ricean channels when the number of transmit and receive antennas converge to +∞ at the same rate. Our approach is based on the extensive use of the Stieljès transform of the Gram matrix of the channel matrix, and is inspired by previous works of Girko in the context of simpler models. We g...

When the iteration proceeds, the size l of labeled set L will grow larger and larger, so inverting the l × l matrix KL,L (KL,L is the sub-matrix of K corresponding to L) at scratch under each iteration is very inefficient. Here we tackle this computational issue by incrementally updating K−1 L,L based on the previous inverting result. As our submission, T is used to denote the curriculum set wi...

In this article we present a statistical version of the Candès-Tao restricted isometry property (SRIP for short) which holds in general for any incoherent dictionary which is a disjoint union of orthonormal bases. In addition, we show that, under appropriate normalization, the eigenvalues of the associated Gram matrix fluctuate around λ = 1 according to the Wigner semicircle distribution. The r...

This is work in progress with Yael Karshon. We develop a localization formula in equivariant cohomology which generalizes both the classical Duistermaat-Heckman formula and the localization formula of Paradan and Woodward for the norm-square of the moment map. Applying a case of our formula to a toric variety, we recover the classical Brianchon-Gram decomposition of a polytope, thus answering a...

In this paper we analyze the relationships between the eigenvalues of the m x m Gram matrix K for a kernel k(·, .) corresponding to a sample Xl, ... ,Xm drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem. We bound the differences between the two spectra and provide a performance bound on kernel peA.

In this paper we formulate and prove a statistical version of the Candès-Tao restricted isometry property (SRIP for short) which holds in general for any incoherent dictionary which is a disjoint union of orthonormal bases. In addition, we prove that, under appropriate normalization, the eigenvalues of the associated Gram matrix fluctuate around λ = 1 according to the Wigner semicircle distribu...

The automorphism group of the Barnes-Wall lattice Lm in dimension 2 m (m 6= 3) is a subgroup of index 2 in a certain “Clifford group” of structure 2 + .O (2m, 2). This group and its complex analogue CIm of structure (2 + YZ8).Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modul...

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight q per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram deter...